Slopes
A researcher is investigating the relationship between the number of hours a student studies and their exam score. They collect data from a sample of students and perform a linear regression analysis. The resulting regression equation is , where is the predicted exam score and is the nu...
Which of the following scenarios best illustrates the identification of explanatory and response variables?
A scatterplot shows the relationship between the number of rainy days in a month and the number of umbrellas sold. The data points are clustered closely around a line that slopes upwards. Which of the following best describes the relationship?
A residual plot shows a distinct curved pattern. What condition for inference about the slope of the regression line is most likely violated?
A researcher is checking conditions for inference for linear regression. They observe that the residuals are clustered around the regression line for small values of x, but spread out more for larger values of x. Which condition is likely violated?
A study is conducted to investigate the relationship between hours of exercise per week and resting heart rate. The researchers collect data from a sample of individuals, but realize that all participants are members of the same gym. Which condition for inference is most likely violated?
A 95% confidence interval for the slope of a regression line is (2.5, 4.0). Which of the following is the correct interpretation of this interval?
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Given the following summary statistics for a linear regression: sample size , slope , standard error of the slope , and critical t-value . Calculate the 95% confidence interval for the slope.
A researcher is testing the hypothesis that there is no linear relationship between two variables. Which of the following is the correct null and alternative hypothesis for a t-test for the slope?
Given a t-statistic of 2.5 and a standard error of the slope of 0.5, calculate the estimated slope.